If `2a+3b+6c-0,(a,b,c in R)` then the quadratic equation `ax^(2)+bx+c-0` has

If a + b + c = 0 then the quadratic equation 3ax^(2) + 2bx + c = 0 has

The quadratic equation ax^(2)+bx+c=0 has real roots if:

If a,b,c in R and a+b+c=0, then the quadratic equation 3ax^(2)+2bx+c=0 has (a) at least one root in [0,1] (b) at least one root in [1,2](c) at least one root in [(3)/(2),2] (d) none of these

If a+b + c = 0, then show that the quadratic equation 3ax^(2) + 2bx +c=0 has at least one root in [0,1].

Let a,b,c in R and a ne 0 be such that (a + c)^(2) lt b^(2) ,then the quadratic equation ax^(2) + bx +c =0 has